[tex]x=2y[/tex] and [tex]x=y^3[/tex] intersect when
[tex]2y=y^3\implies y^3-2y=y(y^2-2)=y(y-\sqrt2)(y+\sqrt2)=0[/tex]
[tex]\implies y=0\text{ or }y=\sqrt2\text{ or }y=-\sqrt2[/tex]
We omit the negative root, since we only care for [tex]y\ge0[/tex].
In the interval (0, √2), we have [tex]y^3<2y[/tex]. Then the volume is given by the integral
[tex]\displaystyle\pi\int_0^{\sqrt2}(2y)^2-(y^3)^2\,\mathrm dy=\pi\int_0^{\sqrt2}4y^2-y^6\,\mathrm dy[/tex]
and so the volume is (32√2)/21 π.
100 POINTS
PLEASE PROVIDE STEPS.
THANK YOU!!!
Answer:
⅓ m/s
Step-by-step explanation:
Area of a square is:
A = s²
Take derivative of both sides with respect to time:
dA/dt = 2s ds/dt
Given that dA/dt = 6 m²/s and s = 9 m:
6 m²/s = 2 (9 m) ds/dt
ds/dt = ⅓ m/s
The Formula of the area of a square: A = bh or A = s^2
Solution:
~Take derivative of both sides
da/dt = 2s * ds/dt
~Use given values (6m^2/s and 9m)
6 = 2(9) * ds/dt
~Simplify
1/3m/s = ds/dt
Best of Luck!
Priscilla’s grandmother’s fruit salad recipe calls for one part apple, one part orange, four parts strawberry, two parts cherry, and three parts grape. Priscilla uses the same measuring cup to measure all of the fruit, so one part is equal to one cup of diced fruit. In this exercise, you will compare the quantities in the recipe to understand ratios better.
Answer:
There are 11 parts of fruit: 4-strawberry, 3- grape, 2, cherry, 1- apple, 1-orange 4/11 from the entine quantity of fruits- strawberry
3/11-grapes
2/11- cherries
1/11- apples
1/11- oranges } ⇒ the quantity of oranges and apples are equal Hope it helps ;>
Identify the graph of the equation... Then find q to the nearest degree.
16x^2+2xy+y^2-16=0
Answer:
ellipse ; 4 degrees
Step-by-step explanation:
edge’s possible answer 2020
May someone please show me how to complete this problem? Thank you!
7 - 3[( n3 + 8 n ) ÷ (- n ) + 9 n2 ]
A) -24 n2 + 31
B) n3 - 24 n2 + 31
C) 9 n2 - 24 n + 7
21 n + 31
To the nearest tenth of a cubic centimeter, what is the volume of
the sphere if r = 17 cm?
Answer:
V≈20579.53
Step-by-step explanation:
[tex]V=\frac{4}{3} \pi r^3[/tex]
The following dot plot shows the pulse rates of runners after finishing a marathon:
dot plot with title of Pulse Rates of Marathon Runners, Pulse Rate on the x axis, and Number of Runners on the y axis with 1 dot over 150, 3 dots over 160, 5 dots over 165, 4 dots over 175
Which of the following data sets is represented in the dot plot?
{150, 160, 160, 160, 165, 165, 165, 165, 165, 175, 175, 175, 175}
{150, 160, 165, 175}
{1, 3, 5, 4}
{150, 160, 162, 164, 165, 165, 166, 167, 168, 175, 174, 176, 175}
Answer:
First one
Step-by-step explanation:
1 dot over 150: 150 once
3 dots over 160: 160 thrice
5 dots over 165: 165 five times
4 dots over 175: 175 four times
{150, 160, 160, 160, 165, 165, 165, 165, 165, 175, 175, 175, 175}
The data sets that represents the dot plot is,{150, 160, 160, 160, 165, 165, 165, 165, 165, 175, 175, 175, 175}.
We have given the,
The following dot plot shows the pulse rates of runners after finishing a marathon.
What is the Pulse Rate?A normal resting heart rate for adults ranges from 60 to 100 beats per minute.
dot plot with the title of Pulse Rates of Marathon Runners, Pulse Rate.
on the x-axis, and the Number of Runners on the y axis with 1 dot over 150, 3 dots over 160, 5 dots over 165, and 4 dots over 175.
1 dot over 150: 150 once 3 dots over 160: 160 thrice 5 dots over 165: 165 five times 4 dots over 175: 175 four times.
Therefore the data sets which represent the dot plot is,{150, 160, 160, 160, 165, 165, 165, 165, 165, 175, 175, 175, 175}
Therefore option first is correct.
To learn more about the dot plot visit:
https://brainly.com/question/24375372
#SPJ2
Find the area of the triangle
Answer:
84mm
Step-by-step explanation:
Formula of a triangle:
A =bh/2
A=14(12)/2
A=168/2
A=84mm
Consider the initial value problem y' − 9 2 y = 9t + 2et, y(0) = y0. Find the value of y0 that separates solutions that grow positively as t → [infinity] from those that grow negatively. (A computer algebra system is recommended. Round your answer to three decimal places.) y0 = How does the solution that corresponds to this critical value of y0 behave as t → [infinity]?
1, The corresponding solution converges to the function y = 9t.
2. The corresponding solution will decrease without bound.
3. The corresponding solution converges to the function y = −9t.
4. The corresponding solution converges to the function y = 0. The corresponding solution will increase without bound.
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
In ΔXYZ, the measure of ∠Z=90°, the measure of ∠X=57°, and XY = 8 feet. Find the length of YZ to the nearest tenth of a foot.
Answer:
21
Step-by-step explanation:
Answer:
6.7
Step-by-step explanation:
148, 139, 109, 146, 141, 179, 187, 131, 149, 141 What is the mean absolute deviation of the data set
Answer:
The mean absolute deviation is 15
Step-by-step explanation:
First you have to find the mean, which in this case is 147.
Then you need to find the difference between each individual number and the mean. Once you have all the diffences written down, you need to add all the differences together. If you take the sum of the differences and divide them by the mean, you'll get your answer!
Let me know if that makes sense! :)
In a random sample of 28 people, the mean commute time to work was 31.7 minutes and the standard deviation was 7.2 minutes. Assume the population is normally distributed and use a t-distribution to construct a 80% confidence interval for the population mean mu. What is the margin of error of mu? Interpret the results.
Answer:
a)The 80% of confidence interval for the Population 'μ' is
(29.9121 ,33.4879)
b) Margin of error of mean ' 'μ' is = 1.7879
Step-by-step explanation:
step(i):-
Given random sample 'n' =28
The mean of the sample x⁻ =31.7 min
The standard deviation of the sample's' =7.2
Step(ii):-
80% of confidence intervals:
The 80% of confidence interval for the Population 'μ' is determined by
[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{s}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{s}{\sqrt{n} } )[/tex]
Degrees of freedom
γ = n-1 = 28-1 =27
[tex]t_{\frac{\alpha }{2} } = t_{\frac{0.20}{2} } = t_{0.1} = 1.314[/tex]
The 80% of confidence interval for the Population 'μ' is determined by
[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{s}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{s}{\sqrt{n} } )[/tex]
[tex](31.7-1.314 X \frac{7.2}{\sqrt{28} } , 31.7+1.314 X\frac{7.2}{\sqrt{28} } )[/tex]
(31.7 -1.7879 , 31.7 +1.7879)
(29.9121 ,33.4879)
b)
Margin of error of mean is determined by
[tex]M.E = {\frac{t_{\frac{\alpha }{2} } s}{\sqrt{n} } }[/tex]
[tex]M.E = {\frac{1.314 X 7.2}{\sqrt{28} } }[/tex]
Margin of error =1.7879
If f(x) = 6x - 5 and (x) = -x + 1 , what is the value of f(g(-3)).
Answer:
19
Step-by-step explanation:
f(x) = 6x - 5
g (x) = -x + 1
f(g(-3))
g(-3) = - (-3) +1 = 3+1 = 4
f(g(-3) = f(4))
f(4)= 6(4) -5 = 24-5 = 19
2. Two researchers, Beth and Frank, ask a random sample of teenagers whether or not they had
been to the movies in the last month. They find that their sample proportion (p) of teens who
said yes was .8 (80%) When they construct a confidence interval based on this sample
proportion, Beth comes up with (.73, 87) while Frank gets (175, 89). Indicate which interval
has to be wrong, and explain your choice. (4 pts)
Answer:
Frank's confidence interval, (.75, .89) has to be wrong.
The explanation is presented below.
Step-by-step explanation:
The Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean.
So, a sample proportion of 80% indicates that Beth's interval of (.73, .87) gives a margin of error of 7%.
Making the lower limit of the interval be
(Sample proportion) - (Margin of error) = 80 - 7 = 73%
Upper limit of the interval = (Sample proportion) + (Margin of error) = 80 + 7 = 87%
Hence, this confidence interval is plausible for the survey carried out.
But Frank's interval of (.75, .89) doesn't work with the definition of a confidence interval given above. The range has to be equally spread around the mean with (lower limit, upper limit). The lower limit cannot be 75 and the upper limit 89.
If the lower limit is truly 75, the margin of error has to be (80 - 75), 5%. And the corresponding upper limit should be (80 + 5), 85%.
Frank's interval as (.75, .85) would have been more plausible.
And if the upper limit is truly 89%, the fiitting lower limit, judging by the distance of the upper limit from the sample proportion (89 - 80 = 9%), should be (80 - 9), 71%. Frank's interval as (.71, .89) would also have been more plausible.
Hope this Helps!!!
What is the surface area of a hemisphere with radius 3? Round to the tenths.
Answer:
56.52
Step-by-step explanation:
Area of hemisphere = 2πr^2
Radius = 3
= 2×3.14×3×3
= 56.52
hope it helps!
A company makes car batteries and claims 80% of its ABC batteries are good for 70 months or longer. Assume that this claim is true. Let p ˆ be the proportion in a sample of 100 such ABC batteries. What is the probability that this sample proportion is within 0.05 of the population proportion.
Answer:
78.88% probability that this sample proportion is within 0.05 of the population proportion
Step-by-step explanation:
We need to understand the normal probability distribution and the central limit theorem to solve this question.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For proportion p in a sample of size n, we have that [tex]\mu = p, s = \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this question:
[tex]p = 0.8, n = 100[/tex]
So
[tex]\mu = 0.8, s = \sqrt{\frac{0.8*0.2}{100}} = 0.04[/tex]
What is the probability that this sample proportion is within 0.05 of the population proportion.
This is the pvalue of Z when X = 0.8 + 0.05 = 0.85 subtracted by the pvalue of Z when X = 0.8 - 0.05 = 0.75.
X = 0.85
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.85 - 0.8}{0.04}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a pvalue of 0.8944.
X = 0.75
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.75 - 0.8}{0.04}[/tex]
[tex]Z = -1.25[/tex]
[tex]Z = -1.25[/tex] has a pvalue of 0.1056.
0.8944 - 0.1056 = 0.7888
78.88% probability that this sample proportion is within 0.05 of the population proportion
Assume the competing hypotheses take the following form: H0: µ1 – µ2 = 0, HA: µ1 – µ2 ≠ 0, where µ1 is the population mean for population 1 and µ2 is the population mean for population 2. Also assume that the populations are normally distributed and that the observations in the two samples are independent. The population variances are not known but are assumed equal. Which of the following expressions is appropriate test statistic?
a. taf
b. 2
c. 1-2 21 n
d. täf 2 t1
Answer:
[tex]t=\frac{\bar x_1- \bar x_2}{\sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2} } }[/tex]
Step-by-step explanation:
H0: µ1 – µ2 = 0
HA: µ1 – µ2 ≠ 0
We have given,
The population variances are not known and cannot be assumed equal.
The test statistic for the test is
[tex]t=\frac{\bar x_1- \bar x_2}{\sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2} } }[/tex]
Where,
[tex]\bar x_1[/tex] = sample meaan of population 1
[tex]\bar x_2[/tex] = sample mean of population 2
[tex]n_1[/tex] = sample size of population 1
[tex]n_2[/tex] = sample size of population 2
Therefore, this is the test
[tex]t=\frac{\bar x_1- \bar x_2}{\sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2} } }[/tex]
What number should be added to both sides of the equation to complete the square? x2 – 10x = 7
Answer:
25
Step-by-step explanation:
x^2 – 10x = 7
Take the coefficient of x
-10
Divide by 2
-10/2 = 5
Square it
5^2 = 25
Add this to both sides
x^2 – 10x+25 = 7+25
Lydia bought a shirt at 20% off its retail price of $40. She paid 5% tax on the price after the discount. How much did Lydia paid for the shirt?
Answer:
33.60
Step-by-step explanation:
First determine the discount
40 * 20%
40 *.2 =8
The discount is 8
40-8 = 32
The shirt was 32 dollars before tax
Now find the tax
32 * 5%
32*.05 =1.60
Add the tax to the sale price
32+1.60
33.60
Answer:
33.6
Step-by-step explanation:
40-20%=32
32+5%=33.6
Which expresion is not equivalent to 8 +(n-4)
Answer:
The answer to this is n+4.
Step-by-step explanation:
There are five families that each have one child. Each of them hires Riley as a babysitter. Because the children she babysits are different ages, Riley charges each family a different amount. To visualize her earnings, Riley recorded and plotted her pay from each job. Using the scatterplot, calculate her average rate of pay.
Answer:
Average Rate of Pay = $ 5.23 /hr
Step-by-step explanation:
We have a data in form of Hours of Baby Sitting and Amount of Pay. Since the Amount of pay depends upon the Hours of Baby Sitting. Thus, we take y = Amount of Pay, while x = Hours of Baby Sitting. So, the data becomes:
x (Hours) = 12 13 16 17 20
y ($) = 54 56 65 64 100
The statistical data calculated is:
∑x = 78, ∑x² = 1258, ∑y = 339, ∑xy = 5504, n = no. of data points = 5
Now, we use linear regression model to fit a straight line to this data.
y = a + bx --------- eqn (1)
where,
b = [ n∑xy - ∑x.∑y]/[n∑x² -(∑x)²]
b = [ (5)(5504) - (78)(339)]/[(5)(1258) - (78)²]
b = 5.23
and,
a = (∑xy - b∑x²)/∑x
a = [5504 - (5.23)(1258)]/78
a = -13.83
Therefore, eqn (1) becomes:
y = -13.83 + 5.23x
The graph plot of this straight line fit is provided in the attachments.
Now, we derivate the equation with respect to x, to get the average rate of pay:
Average Rate of Pay = dy/dx = d/dx(-13.83 + 5.23x)
Average Rate of Pay = $ 5.23 /hr
karen brought 3/8 of a gallon of ice tea to a party. Robin brought 15/16 of a gallon of ice tea to the same party. How much ice tea did they have together?
Answer:
1 5/16 gallon
Step-by-step explanation:
Gallon of ice brought by Karen = 3/8
Gallon of ice brought by Robin = 15/16
Total ice team brought by them is sum of Gallon of ice brought by Karen + Gallon of ice brought by Robin
Total ice team brought by Karen and Robin = 3/8 + 15/16
=> 3*2/8*2 + 15/16
we are multiplying with 2 both numerator and denominator in 3/8 so sas the denominator becomes 16 as in other fraction denominator is 16
=> 6/16 + 15/16
=> (6+15)/16 = 21/16
since 21/16 is improper fraction, converting it in mixed fraction we have
21/16 = 1 5/16 gallon
Thus , Karen and Robin have 1 5/16 gallon ice tea together.
Round 299 to the nearest hundred. Enter your answer in the box below.
Answer:
300
Step-by-step explanation:
hundreds tens ones
2 9 9
We look at the tens
It is 5 or higher so we round up the hundreds place
2 becomes 3
300
Answer:
300
Step-by-step explanation:
its obv 300 because 299 is greater than 249 and if it is less than 249 it is rounded to 200.
You are conducting research for a popular blog to find out the proportion of readers who are satisfied with the site's newly designed navigation. You want to make sure that you increase your chances for capturing the true proportion of readers who are satisfied, but the margin of error is too large.
Which of the following would you do?
A. Use a larger confidence level, but choose a smaller margin of error
B. To increase your confidence, you must be willing to accept a smaller margin of error
C. To get a smaller margin of error, you must be willing to accept lower confidence
D. All of the above
Answer: Option(C) is correct option
Explanation:
Margin of error is the factor that occurs in survey for determining random sampling error. It indicates about confidence interval (CI) through describing difference occurring in poll result and actual population value.If there is high margin of error, then confidence is low because poll result will not reflect the actual population result collected through survey.
According to the question, researcher would try to get small margin of error so that lower confidence interval can be acceptable because large confidence interval(CI) will indicate more margin of error.
Other options are incorrect because small margin of error cannot produce increment in confidence or usage of large confidence.Large confidence interval will result in large margin of error. Thus, the correct option is option(c).
1 Which of the following is the correct way to expand a factorial?
A
7! = 7 x 7 x.7 x 7 x 7 x 7 x 7
B
7! = 7 X 6 X 5 X 4 x 3 x 2 x 1
C 7! = 7 x 5 x 3 x1
D
7! = 7
o
Answer:
B
7! = 7 X 6 X 5 X 4 x 3 x 2 x 1
Step-by-step explanation:
n! is the product of all natural numbers until n
7! = 1 × 2 × 3 × 4 × 5 × 6 × 7
The answer is B 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1
how many square feet of of outdoor carpet will we need for this hole?
Answer:
To convert the feet to square feet we have to multiply the length by the width. In which, we should get the answer as well.
Our length is 2ft, since it's a rectangle the other side is 2ft as well.
The width is 3ft, and the other half is 3ft.
So, basically to get the area of the hole, it'd be 3*2=
Which, it's 6sq ft.
Step-by-step explanation:The actual answer is 36. If I am wrong i am sorry ;3
The original price was $12, increased to $15. Find the percent increase
Answer:
25%
Step-by-step explanation:
Take the new price and subtract the original price
15-12 = 3
Divide by the original price
3/12 = .25
Multiply by 100%
25%
The percent increase is 25%
A bag contains 1 yellow, 2 blue, 4 green, and 3 red marbles. A marble is drawn and replaced. Then a
second marble is drawn.
Part A
What is P (blue, then blue)?
Part B
What is P (green, then red)?
Answer:
Step-by-step explanation:
total = 1 + 2 + 4 + 3 = 10
blue then blue = 2/10 * 2/10 = 1/5 * 1/5 = 1/25
green then red = 4/10 * 3/10 = 12/100 = 3/25
What is true when you rent? A.you build equity in your house,B.you are responsible for any repairs,c. You pay fewer up front costs
Answer: C you pay fee fewer upfront cost
Step-by-step explanation:
Ramesh examined the pattern in the table. Powers of 7 Value 7 Superscript 4 2,401 7 Superscript 3 343 7 Superscript 2 49 7 Superscript 1 7 7 Superscript 0 1 7 Superscript negative 1 StartFraction 1 Over 7 EndFraction Ramesh says that based on the pattern 7 Superscript negative 5 = negative 16,807. Which statement explains whether Ramesh is correct? Ramesh is correct because 7 Superscript negative 5 is equivalent to Negative 7 times (negative 7) times (negative 7) times (negative 7) times (negative 7), which has the same value as Negative 16,807. Ramesh is correct because as the exponents decrease, the previous value is divided by 7, so 7 Superscript negative 5 = 1 divided by 7 divided by 7 divided by 7 divided by 7 divided by 7 = negative 16,807. Ramesh is not correct because 7 Superscript negative 5 is equivalent to StartFraction 1 Over 7 Superscript 5 EndFraction, which has the same value as StartFraction 1 Over 7 Superscript 4 EndFraction divided by 7 = StartFraction 1 Over 7 cubed EndFraction = StartFraction 1 Over 343 EndFraction. Ramesh is not correct because as the exponents decrease, the previous value is divided by 7, so 7 Superscript negative 5 = 1 divided by 7 divided by 7 divided by 7 divided by 7 divided by 7 = StartFraction 1 Over 16,807 EndFraction. NEED HELP NOW PLEASE I HAVE ONLY SEEN WRONG ANSWERS
Answer:
D
Step-by-step explanation:
Answer:
D.- Ramesh is not correct because as the exponents decrease, the previous value is divided by 7, so 7^-5 = 1 ÷ 7 ÷ 7 ÷ 7 ÷ 7 ÷ 7 = 1/16,807.
6th grade math! Help me please :))
Subtract 48-19=29 Correct me if I'm wrong.
That means it's 29 cups.
Answer:
29 cups
Step-by-step explanation:
step 1: since the liquid in the photo is shown to go up to between 18 and 20, it has to be 19 cups.
step 2: so she had 48 cups, right? and she used 19. so we have to subtract 19 from 48.
step 3: 48-19 = 29. she has 29 cups left..
i hope this helps!
